Independent Events

Independent Events

Two events are independent if the occurrence of one does not change the probability of the other occurring.
An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head.
If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring.

Specific Multiplication Rule

Only valid for independent events

   P(A and B) = P(A) * P(B)

Example 3:

P(A) = 0.20, P(B) = 0.70, A and B are independent.

	B	B'	Marginal
A	0.14	0.06	0.20
A'	0.56	0.24	0.80
Marginal	0.70	0.30	1.00

The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.